Question

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $v_2$=\frac {n}{m^2}$$v_1 and $a_2$= $\frac {a1}{mn}$ respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

• A. \frac{n^3}{m^3}$$L_1=$L_2$ and \frac{n2}{m}$$T_1=$T_2$
• B. $L_1$=n4/m2$L_2$ and $T_1$=$\frac{n^2}{m}$T2
• C. $L_1$=\frac{n^2}{m}$$L_2 and $T_1$=$\frac{n^4}{m_2}$T2
• D. \frac{n^2}{m}$$L_1=$L_2$ and \frac{n^4}{m^2}$$T_1=$T_2$

Answer 1

Answer: (A)

\frac{n^3}{m^3}$$L_1=$L_2$ and \frac{n2}{m}$$T_1=$T_2$

Answer 2

[L]=$\frac{[v^2]}{[a]}$

So, [v2]2[a2]=$\frac{[\frac{n}{m^2}v_1]^2}{[\frac{a_1}{mn}]}$

[v2]2[a2]=\frac{n^3}{m^3}$$\frac{[v_1]^2}{[a_1]} or [L2]=$\frac{n^3}{m^3}$[L1]

Similarly, [T]=$\frac{[v]}{[a]}$

So, [T2]=$\frac{n^2}{m}$[T1]

$\therefore$ The correct option is (A): \frac{n^3}{m^3}$$L_1=$L_2$ and \frac{n2}{m}$$T_1=$T_2$